Entanglement and mutual information in two-dimensional nonrelativistic field theories

Abstract

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories -this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.

Holographic Entanglement Entropy in NMG

“…In this background, we will prove the existence of a new entangling surface by deforming the geodesic. Consequently, we establish that the existent analysis in this regard [20] requires further attentions. As a final example, in section 5 we investigate the deformation of the entangling surface for the Warped AdS 3 spacetime.…”

“…Moreover, in [17] the authors have shown that, for a particular class of asymptotically AdS spacetimes in four dimensional higher derivative theory, a perturbative modification of AdS geodesic provides the correct entangling surface satisfying the necessary physical boundary conditions. Further analysis in this context can be found in [18][19][20].…”

“…For ν = 1, we recover the AdS 3 spacetime as a special limit of the Lifshitz spacetime (in the appendix A we reproduce the same result using the notation of [20]). Since obtaining an exact solution for non-linear fourth order differential equation like (4.10) is generically difficult, we rather aim to solve the equation using a perturbative technique.…”

Non-local probes in holographic theories with momentum relaxation

“…Although in the case of non-static states the dynamical exponent may appear in the entanglement entropy (see [52,53]). 7,8 7 Also in the case of higher derivative gravity theories, appearance of the dynamical critical exponent in the entanglement entropy was previously reported in [54,55]. 8 See also [56] for related studies in hyperscaling violating backgrounds with momentum relaxation.…”

Entanglement in Lifshitz-type quantum field theories

“…This constructs the very most literature of quantum entanglement in the context of QFTs. Although there have been some attempts so far to analyse the entanglement structure in the non-relativistic cases with z = 1 (see [15][16][17] on the QFT side and [18][19][20][21][22][23] in the context of gauge/gravity duality 1 ), still there are several open questions about the role of z in the entanglement structure of such theories.…”